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Problem 149 from Connelly's corpus: C, Eb, Hb


Problem

Given a point C, a point Eb and a point Hb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Eb and the point Hb, construct a line hb (rule W02);

    % DET: points Eb and Hb are not the same

  2. Using the point Hb and the line hb, construct a line b (rule W10a);

  3. Choose freely a point C on the line b (rule WOnline2)

  4. Using the point C and the point Hb, construct a line m(CHb) (rule W14);

    % DET: points C and Hb are not the same

  5. Using the point Eb and the point Hb, construct a line m(EbHb) (rule W14);

    % DET: points Eb and Hb are not the same

  6. Choose freely a point A on the line b (rule WOnline1)

  7. Using the point A and the point C, construct a point Mb (rule W01);

  8. Using the point Eb and the point Mb, construct a line m(HaHc) (rule W02);

    % DET: points Eb and Mb are not the same

  9. Using the line m(EbHb) and the line m(HaHc), construct a point N (rule W03);

    % NDG: lines m(EbHb) and m(HaHc) are not parallel

    % DET: lines m(EbHb) and m(HaHc) are not the same

  10. Using the point Eb and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Eb and N are not the same

  11. Using the circle k(N,Ma) and the line m(CHb), construct a point Ma and a point Ec (rule W04);

    % NDG: line m(CHb) and circle k(N,Ma) intersect

  12. Using the point C and the point Ma, construct a point B (rule W01);

animation
Construction in GCLC language

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